A stroking cross groove constant velocity universal joint ("cross groove universal joint") typically includes an outer joint member having a plurality of inward facing outer ball grooves alternately tilted in opposite directions relative to an axis of rotation of the outer joint member and an inner joint member inside of the outerjoint member having a plurality of outward facing inner ball grooves alternately tilted in opposite directions relative to an axis of rotation of the inner joint member. The inner and outer ball grooves face each other in crossed pairs with a bearing ball between each crossed pair for torque transfer between the inner and outer joint members. A cage between the inner and outer joint members has a plurality of windows for the bearing balls which closely confine the bearing balls to a plane bisecting the angle of articulation between the axes of rotation of the inner and outer joint members. In a "disc style" cross groove universal joint where the outer joint member is open at both front and back sides thereof, there is a potential for the bearing balls to escape if the inner joint member is accidentally stroked too far inward or outward from a center position during shipping and handling or during installation in an operating environment such as a motor vehicle front wheel drive system. The potential for such escape of the bearing balls may be reduced by increasing the depth of the outer joint member, by fitting retainers on the front and back sides of the outer joint member, or by staking the outer joint member to define stops at the ends of the outer ball grooves. Increasing the depth of the outer joint member or fitting a retainer on the back side thereof are unattractive solutions because adequate running clearance may require changes in the dimensions of structures near the cross groove universal joint. Staking the outer joint member is unattractive because it requires an additional manufacturing operation after the bearing balls and the cage are assembled between the inner and the outer joint members.